Fast Filter Back Projection Algorithm Based on Hexagonal Grid

After optimizing filter back projection (FBP) algorithm of CT with the theory of symmetric transformation group and based on the fact that regular hexagons have the most symmetry axis among all the regular polygons which could pave the two dimensional plane without chink (total six symmetry axis compare three of regular triangle and four of square), a fast reconstruction algorithm is founded to reduce calculating time cost in the back projection part of FBP. Since the back projection part is the major time-consuming part of FBP, the new algorithm accelerates image reconstruction significantly. Compared with the accelerating algorithms appeared recently in the same condition, the reconstruction speed of the proposed method is improved greatly.